Fractions as division and dividing with unit fractions

When you share whole things equally, the answer can be a fraction. If 3 loaves of flatbread are shared by 4 children, each child gets 3 ÷ 4 = 3/4 of a loaf. To see why, cut every loaf into 4 equal quarters. There are 12 quarters, and each child gets 3 of them. So a fraction bar means divide: the numerator is divided by the denominator, a ÷ b = a/b. This works when a is bigger than b too. 5 ÷ 2 = 5/2 = 2 1/2: 5 metres of rope cut into 2 equal pieces gives pieces of 2 1/2 metres. To change an improper fraction into a mixed number, divide the numerator by the denominator: the quotient is the whole part and the remainder is the new numerator. Check by multiplying: 4 × 3/4 = 3.